He hasn’t even signed the birth certificate after 18 months am I wrong to not want his side of family keep her without my supervision?

How could you be wrong? You have a right to your feelings and to your opinion.

You are the baby's mother and you leave your daughter with people you trust. Just because you don't like his mother doesn't make her an un-safe person. She's the baby's grandmother after all and would care for your baby......but at the end of the day, it's your instinct that counts. Why has your partner not signed the certificate? Does he not want to be on it as her father? Why not? You need to sort that out with him. Is he the right person for you to be with?

Why are you asking a Q based on half truth when it's really about your relationship or lack of relationship with his mother that is the real deal here? This type of half hearted disagreement will only escalate given the fact that you are holding his mothers grandchild hostage for whatever the reason is to clearly get her back up. Children being raised this way are tantamount to suffer psychological damage due to the fighting and arguing they hear while growing up based on your insecurities being aired possibly once too often in front of your daughter. They say a child usually follows in their parents footsteps, do you really want you child to go down that path you wished you'd never taken in pairing with such a deadbeat such as her father? Sorry, but that's what I feel after reading your Q.

The father does not sign the birth certificate, so I don't know what you're talking about.
This guy is the one you chose to father your child, and you've chosen to live with him. That's on you. Own it.

You don't punish the child for the acts of it's mother and father. It benefits the child to have it's extended family in it's life to love and support it. Deal with his family without depriving your child of it's extended family.

well thats his business